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<html>
<head>
<title>CapFlow.thy</title>
</head>
<body bgcolor="#ffffff">
<pre><font color="#000000"><span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 1 </font></span><font color="#006699"><strong>theory</strong></font> CapFlow
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 2 </font></span><font color="#009966"><strong>imports</strong></font> Dynamic_model
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 3 </font></span><font color="#009966"><strong>begin</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 4 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 5 </font></span><font color="#006699"><strong>subsection</strong></font> <font color="#6600cc">{* Definitions *}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 6 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 7 </font></span><font color="#006699"><strong>type_synonym</strong></font> max_buffer_size <font color="#000000"><strong>=</strong></font> nat
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 8 </font></span><font color="#006699"><strong>type_synonym</strong></font> buffer_size <font color="#000000"><strong>=</strong></font> nat
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 9 </font></span><font color="#006699"><strong>typedecl</strong></font> Message
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 10 </font></span><font color="#006699"><strong>typedecl</strong></font> Endpoint
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 11 </font></span><font color="#006699"><strong>typedecl</strong></font> Domain
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 12 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 13 </font></span><font color="#006699"><strong>type_synonym</strong></font> domain_id <font color="#000000"><strong>=</strong></font> nat
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 14 </font></span><font color="#006699"><strong>type_synonym</strong></font> domain_name <font color="#000000"><strong>=</strong></font> string
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 15 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 16 </font></span><font color="#006699"><strong>type_synonym</strong></font> endpoint_name <font color="#000000"><strong>=</strong></font> string
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 17 </font></span><font color="#006699"><strong>type_synonym</strong></font> endpoint_id <font color="#000000"><strong>=</strong></font> nat
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 18 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 19 </font></span><font color="#006699"><strong>datatype</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 20 </font></span> right <font color="#000000"><strong>=</strong></font> SEND
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 21 </font></span> <font color="#000000"><strong>|</strong></font>TAKE
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 22 </font></span> <font color="#000000"><strong>|</strong></font>GRANT
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 23 </font></span> <font color="#000000"><strong>|</strong></font>REMOVE
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 24 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 25 </font></span><font color="#006699"><strong>record</strong></font> cap <font color="#000000"><strong>=</strong></font> target <font color="#000000"><strong>::</strong></font> domain_id
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 26 </font></span> rights <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"right set"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 27 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 28 </font></span><font color="#006699"><strong>record</strong></font> Endpoint_Concig <font color="#000000"><strong>=</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 29 </font></span> e_max_buf_size <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"endpoint_id ⇀ max_buffer_size"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 30 </font></span> e_name <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"endpoint_id ⇀ endpoint_name"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 31 </font></span> e_listener <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"endpoint_id ⇀ domain_id"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 32 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 33 </font></span><font color="#006699"><strong>record</strong></font> Domain_Config <font color="#000000"><strong>=</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 34 </font></span> d_name <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"domain_id ⇀ domain_name"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 35 </font></span> d_ep_set <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"domain_id ⇒ endpoint_id set"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 36 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 37 </font></span><font color="#006699"><strong>record</strong></font> Sys_Config <font color="#000000"><strong>=</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 38 </font></span> domconf <font color="#000000"><strong>::</strong></font> Domain_Config
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 39 </font></span> commconf <font color="#000000"><strong>::</strong></font> Endpoint_Concig
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 40 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 41 </font></span><font color="#006699"><strong>subsubsection</strong></font> <font color="#6600cc">{* System state *}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 42 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 43 </font></span><font color="#006699"><strong>record</strong></font> State <font color="#000000"><strong>=</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 44 </font></span> <font color="#cc0000">(*caps :: "domain_id ⇒ domain_id ⇒ right set"*)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 45 </font></span> caps <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"domain_id ⇒ cap set"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 46 </font></span> e_msgs <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"endpoint_id ⇒ Message set"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 47 </font></span> e_buf_size <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"endpoint_id ⇀ buffer_size"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 48 </font></span> domain_endpoint <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"endpoint_id ⇀ domain_id "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 49 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 50 </font></span><font color="#006699"><strong>datatype</strong></font> Event <font color="#000000"><strong>=</strong></font> Client_Lookup_Endpoint_Name domain_id endpoint_name
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 51 </font></span> <font color="#000000"><strong>|</strong></font> Send_Queuing_Message domain_id endpoint_id Message
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 52 </font></span> <font color="#000000"><strong>|</strong></font> Receive_Queuing_Message domain_id endpoint_id
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 53 </font></span> <font color="#000000"><strong>|</strong></font> Get_My_Endpoints_Set domain_id
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 54 </font></span> <font color="#000000"><strong>|</strong></font> Get_Caps domain_id
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 55 </font></span> <font color="#000000"><strong>|</strong></font> Grant_Endpoint_Cap domain_id cap cap
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 56 </font></span> <font color="#000000"><strong>|</strong></font> Remove_Cap_Right domain_id cap right
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 57 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 58 </font></span><font color="#006699"><strong>subsubsection</strong></font> <font color="#6600cc">{* Utility Functions used for Event Specification *}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 59 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 60 </font></span><font color="#006699"><strong>definition</strong></font> get_domain_name_from_domain_id <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ domain_id ⇒ domain_name option"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 61 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_domain_name_from_domain_id sc did ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 62 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 63 </font></span><font color="#ff00cc"> dm_conf = (domconf sc)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 64 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 65 </font></span><font color="#ff00cc"> if((d_name dm_conf) did ≠ None )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 66 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 67 </font></span><font color="#ff00cc"> ((d_name dm_conf) did )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 68 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 69 </font></span><font color="#ff00cc"> None"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 70 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 71 </font></span><font color="#006699"><strong>definition</strong></font> get_endpoints_from_domain_id <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ domain_id ⇒ endpoint_id set"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 72 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_endpoints_from_domain_id sc did ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 73 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 74 </font></span><font color="#ff00cc"> dm_conf = (domconf sc)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 75 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 76 </font></span><font color="#ff00cc"> if((d_name dm_conf) did ≠ None )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 77 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 78 </font></span><font color="#ff00cc"> ((d_ep_set dm_conf) did )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 79 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 80 </font></span><font color="#ff00cc"> {}"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 81 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 82 </font></span><font color="#006699"><strong>definition</strong></font> get_domain_id_from_domain_name <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ domain_name ⇒ domain_id option"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 83 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_domain_id_from_domain_name sc dname ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 84 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 85 </font></span><font color="#ff00cc"> dm_conf = (domconf sc) </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 86 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 87 </font></span><font color="#ff00cc"> if(∃did. the((d_name dm_conf) did) = dname )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 88 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 89 </font></span><font color="#ff00cc"> Some (SOME did. the((d_name dm_conf) did) = dname)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 90 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 91 </font></span><font color="#ff00cc"> None"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 92 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 93 </font></span><font color="#006699"><strong>definition</strong></font> get_listener_id_from_endpoint_id <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ endpoint_id ⇒ domain_id option"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 94 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_listener_id_from_endpoint_id sc eid ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 95 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 96 </font></span><font color="#ff00cc"> ep_conf = (commconf sc)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 97 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 98 </font></span><font color="#ff00cc"> if((e_listener ep_conf) eid ≠ None )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 99 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 100 </font></span><font color="#ff00cc"> ((e_listener ep_conf) eid )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 101 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 102 </font></span><font color="#ff00cc"> None"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 103 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 104 </font></span><font color="#006699"><strong>definition</strong></font> get_endpoint_name_from_endpoint_id <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ endpoint_id ⇒ endpoint_name option"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 105 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_endpoint_name_from_endpoint_id sc eid ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 106 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 107 </font></span><font color="#ff00cc"> ep_conf = (commconf sc)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 108 </font></span><font color="#ff00cc"> in </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 109 </font></span><font color="#ff00cc"> if((e_name ep_conf) eid ≠ None )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 110 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 111 </font></span><font color="#ff00cc"> ((e_name ep_conf) eid )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 112 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 113 </font></span><font color="#ff00cc"> None"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 114 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 115 </font></span><font color="#006699"><strong>definition</strong></font> get_endpoint_id_from_endpoint_name <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ endpoint_name ⇒ endpoint_id option"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 116 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_endpoint_id_from_endpoint_name sc ename ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 117 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 118 </font></span><font color="#ff00cc"> ep_conf = (commconf sc)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 119 </font></span><font color="#ff00cc"> in </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 120 </font></span><font color="#ff00cc"> if(∃eid. the((e_name ep_conf) eid) = ename )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 121 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 122 </font></span><font color="#ff00cc"> Some (SOME eid. the((e_name ep_conf) eid) = ename )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 123 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 124 </font></span><font color="#ff00cc"> None"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 125 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 126 </font></span><font color="#006699"><strong>definition</strong></font> get_endpoint_max_bufsize_from_sc_by_id <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ endpoint_id ⇒ max_buffer_size option"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 127 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_endpoint_max_bufsize_from_sc_by_id sc eid ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 128 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 129 </font></span><font color="#ff00cc"> ep_conf = (commconf sc)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 130 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 131 </font></span><font color="#ff00cc"> if((e_max_buf_size ep_conf) eid ≠ None )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 132 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 133 </font></span><font color="#ff00cc"> ((e_max_buf_size ep_conf) eid )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 134 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 135 </font></span><font color="#ff00cc"> None"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 136 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 137 </font></span><font color="#006699"><strong>definition</strong></font> is_a_domain <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ domain_id ⇒ bool"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 138 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"is_a_domain sc did ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 139 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 140 </font></span><font color="#ff00cc"> dm_conf = (domconf sc)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 141 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 142 </font></span><font color="#ff00cc"> if((d_name dm_conf) did ≠ None )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 143 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 144 </font></span><font color="#ff00cc"> True</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 145 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 146 </font></span><font color="#ff00cc"> False"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 147 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 148 </font></span><font color="#006699"><strong>definition</strong></font> is_an_endpoint <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ endpoint_id ⇒ bool"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 149 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"is_an_endpoint sc eid ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 150 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 151 </font></span><font color="#ff00cc"> ep_conf = (commconf sc)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 152 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 153 </font></span><font color="#ff00cc"> if((e_name ep_conf) eid ≠ None )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 154 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 155 </font></span><font color="#ff00cc"> True</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 156 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 157 </font></span><font color="#ff00cc"> False"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 158 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 159 </font></span><font color="#006699"><strong>definition</strong></font> is_an_endpoint_of_domain <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ endpoint_id ⇒ domain_id ⇒ bool"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 160 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"is_an_endpoint_of_domain sc eid did ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 161 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 162 </font></span><font color="#ff00cc"> dm_conf = (domconf sc) </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 163 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 164 </font></span><font color="#ff00cc"> if(eid ∈ ((d_ep_set dm_conf) did))</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 165 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 166 </font></span><font color="#ff00cc"> True</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 167 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 168 </font></span><font color="#ff00cc"> False"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 169 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 170 </font></span><font color="#006699"><strong>definition</strong></font> is_an_endpoint_of_listener <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ endpoint_id ⇒ domain_id ⇒ bool"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 171 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"is_an_endpoint_of_listener sc eid did ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 172 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 173 </font></span><font color="#ff00cc"> ep_conf = (commconf sc)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 174 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 175 </font></span><font color="#ff00cc"> if(the((e_listener ep_conf) eid) = did )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 176 </font></span><font color="#ff00cc"> then </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 177 </font></span><font color="#ff00cc"> True </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 178 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 179 </font></span><font color="#ff00cc"> False"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 180 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 181 </font></span><font color="#006699"><strong>definition</strong></font> get_domain_cap_set_from_domain_id <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ cap set"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 182 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s did ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 183 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 184 </font></span><font color="#ff00cc"> cap_by_id = caps s</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 185 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 186 </font></span><font color="#ff00cc"> cap_by_id did</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 187 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 188 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 189 </font></span><font color="#006699"><strong>definition</strong></font> get_msg_set_from_endpoint_id <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ endpoint_id ⇒ Message set"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 190 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_msg_set_from_endpoint_id s eid ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 191 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 192 </font></span><font color="#ff00cc"> msg_by_id = e_msgs s</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 193 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 194 </font></span><font color="#ff00cc"> msg_by_id eid</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 195 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 196 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 197 </font></span><font color="#006699"><strong>definition</strong></font> get_buf_size_from_endpoint_id <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ endpoint_id ⇒ buffer_size option"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 198 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_buf_size_from_endpoint_id s eid ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 199 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 200 </font></span><font color="#ff00cc"> buf_size_by_id = e_buf_size s</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 201 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 202 </font></span><font color="#ff00cc"> buf_size_by_id eid</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 203 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 204 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 205 </font></span><font color="#006699"><strong>definition</strong></font> endpoint_is_full <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ State ⇒ endpoint_id ⇒ bool"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 206 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"endpoint_is_full sc s eid ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 207 </font></span><font color="#ff00cc"> get_buf_size_from_endpoint_id s eid </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 208 </font></span><font color="#ff00cc"> = get_endpoint_max_bufsize_from_sc_by_id sc eid"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 209 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 210 </font></span><font color="#006699"><strong>definition</strong></font> get_endpoints_of_domain <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ endpoint_id set"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 211 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s did ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 212 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 213 </font></span><font color="#ff00cc"> dom_ep = domain_endpoint s</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 214 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 215 </font></span><font color="#ff00cc"> {x. dom_ep x = Some did}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 216 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 217 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 218 </font></span><font color="#006699"><strong>definition</strong></font> get_domain_id_from_endpoint <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ endpoint_id ⇒ domain_id option"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 219 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_domain_id_from_endpoint s eid ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 220 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 221 </font></span><font color="#ff00cc"> dom_ep = domain_endpoint s</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 222 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 223 </font></span><font color="#ff00cc"> dom_ep eid</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 224 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 225 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 226 </font></span><font color="#006699"><strong>definition</strong></font> get_endpoint_msg_set_of_domain <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ Message set"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 227 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_endpoint_msg_set_of_domain s did ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 228 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 229 </font></span><font color="#ff00cc"> dom_ep = domain_endpoint s;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 230 </font></span><font color="#ff00cc"> eid_set = get_endpoints_of_domain s did;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 231 </font></span><font color="#ff00cc"> msg_of_ep = e_msgs s</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 232 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 233 </font></span><font color="#ff00cc"> {x. ∃e. e∈eid_set ∧ x ∈ msg_of_ep e}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 234 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 235 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 236 </font></span><font color="#006699"><strong>definition</strong></font> interferes <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"domain_id ⇒ State ⇒ domain_id ⇒ bool"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 237 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"interferes w s v ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 238 </font></span><font color="#ff00cc"> if( w = v</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 239 </font></span><font color="#ff00cc"> ∨ (∃c. c∈(get_domain_cap_set_from_domain_id s w) ∧ target c = v))</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 240 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 241 </font></span><font color="#ff00cc"> True</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 242 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 243 </font></span><font color="#ff00cc"> False</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 244 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 245 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 246 </font></span><font color="#006699"><strong>subsubsection</strong></font><font color="#6600cc">{* Event specification *}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 247 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 248 </font></span><font color="#006699"><strong>definition</strong></font> client_lookup_endpoint_name <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ State </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 249 </font></span><font color="#ff00cc"> ⇒ domain_id ⇒ endpoint_name ⇒ (State × endpoint_id option)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 250 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"client_lookup_endpoint_name sc s did ename ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 251 </font></span><font color="#ff00cc"> if(get_endpoint_id_from_endpoint_name sc ename ≠ None)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 252 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 253 </font></span><font color="#ff00cc"> (s, get_endpoint_id_from_endpoint_name sc ename)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 254 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 255 </font></span><font color="#ff00cc"> (s, None)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 256 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 257 </font></span><font color="#006699"><strong>definition</strong></font> send_queuing_message <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ endpoint_id ⇒ Message ⇒ (State × bool)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 258 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"send_queuing_message s did eid m ≡</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 259 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 260 </font></span><font color="#ff00cc"> dom_ep = domain_endpoint s;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 261 </font></span><font color="#ff00cc"> dst_dom = dom_ep eid;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 262 </font></span><font color="#ff00cc"> emsgs = e_msgs s;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 263 </font></span><font color="#ff00cc"> msg_set = get_msg_set_from_endpoint_id s eid;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 264 </font></span><font color="#ff00cc"> new_msg_set = insert m msg_set</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 265 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 266 </font></span><font color="#ff00cc"> if(get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 267 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 268 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 269 </font></span><font color="#ff00cc"> (s⦇</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 270 </font></span><font color="#ff00cc"> e_msgs := emsgs(eid := new_msg_set)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 271 </font></span><font color="#ff00cc"> ⦈, False) </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 272 </font></span><font color="#ff00cc"> else </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 273 </font></span><font color="#ff00cc"> (s, False)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 274 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 275 </font></span><font color="#006699"><strong>definition</strong></font> receive_queuing_message <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ endpoint_id ⇒ (State × Message option)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 276 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"receive_queuing_message s did eid ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 277 </font></span><font color="#ff00cc"> if(get_domain_id_from_endpoint s eid = Some did)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 278 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 279 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 280 </font></span><font color="#ff00cc"> emsgs = e_msgs s;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 281 </font></span><font color="#ff00cc"> msg_set = get_msg_set_from_endpoint_id s eid;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 282 </font></span><font color="#ff00cc"> m = SOME x. x∈msg_set;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 283 </font></span><font color="#ff00cc"> new_msg_set = msg_set - {m} </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 284 </font></span><font color="#ff00cc"> in </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 285 </font></span><font color="#ff00cc"> (s⦇</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 286 </font></span><font color="#ff00cc"> e_msgs := emsgs(eid := new_msg_set)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 287 </font></span><font color="#ff00cc"> ⦈, Some m)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 288 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 289 </font></span><font color="#ff00cc"> (s, None)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 290 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 291 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 292 </font></span><font color="#006699"><strong>definition</strong></font> get_my_endpoints_set <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ (State × endpoint_id set)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 293 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_my_endpoints_set s did ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 294 </font></span><font color="#ff00cc"> if(get_endpoints_of_domain s did ≠ {})</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 295 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 296 </font></span><font color="#ff00cc"> (s, get_endpoints_of_domain s did)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 297 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 298 </font></span><font color="#ff00cc"> (s, {})</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 299 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 300 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 301 </font></span><font color="#006699"><strong>definition</strong></font> get_caps <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ (State × cap set)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 302 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_caps s did ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 303 </font></span><font color="#ff00cc"> (s, get_domain_cap_set_from_domain_id s did)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 304 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 305 </font></span><font color="#006699"><strong>definition</strong></font> grant_endpoint_cap <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ cap ⇒ cap ⇒ (State × bool)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 306 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"grant_endpoint_cap s did grant_cap dst_cap ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 307 </font></span><font color="#ff00cc"> if(grant_cap∈get_domain_cap_set_from_domain_id s did </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 308 </font></span><font color="#ff00cc"> ∧ GRANT∈rights grant_cap</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 309 </font></span><font color="#ff00cc"> ∧ target grant_cap ≠ target dst_cap</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 310 </font></span><font color="#ff00cc"> ∧ dst_cap∈get_domain_cap_set_from_domain_id s did)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 311 </font></span><font color="#ff00cc"> then </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 312 </font></span><font color="#ff00cc"> let </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 313 </font></span><font color="#ff00cc"> did_dst = target grant_cap;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 314 </font></span><font color="#ff00cc"> caps0 = caps s;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 315 </font></span><font color="#ff00cc"> cs_dst = get_domain_cap_set_from_domain_id s did_dst </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 316 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 317 </font></span><font color="#ff00cc"> (s⦇</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 318 </font></span><font color="#ff00cc"> caps := caps0(did_dst := (insert dst_cap cs_dst))</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 319 </font></span><font color="#ff00cc"> ⦈, True) </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 320 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 321 </font></span><font color="#ff00cc"> (s, False)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 322 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 323 </font></span><font color="#006699"><strong>definition</strong></font> get_takable_caps <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ cap ⇒ (State × cap set)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 324 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"get_takable_caps s did take_cap ≡</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 325 </font></span><font color="#ff00cc"> if(take_cap ∈ get_domain_cap_set_from_domain_id s did </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 326 </font></span><font color="#ff00cc"> ∧ TAKE ∈ rights take_cap)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 327 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 328 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 329 </font></span><font color="#ff00cc"> did_dst = target take_cap</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 330 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 331 </font></span><font color="#ff00cc"> (s, get_domain_cap_set_from_domain_id s did_dst)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 332 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 333 </font></span><font color="#ff00cc"> (s, {})"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 334 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 335 </font></span><font color="#006699"><strong>definition</strong></font> take_endpoint_cap <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ cap ⇒ cap ⇒ (State × bool)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 336 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"take_endpoint_cap s did take_cap dst_cap ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 337 </font></span><font color="#ff00cc"> if(take_cap ∈ get_domain_cap_set_from_domain_id s did </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 338 </font></span><font color="#ff00cc"> ∧ TAKE ∈ rights take_cap </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 339 </font></span><font color="#ff00cc"> ∧ interferes did s (target dst_cap)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 340 </font></span><font color="#ff00cc"> ∧ dst_cap ∈ get_domain_cap_set_from_domain_id s (target take_cap))</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 341 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 342 </font></span><font color="#ff00cc"> let </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 343 </font></span><font color="#ff00cc"> caps0 = caps s;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 344 </font></span><font color="#ff00cc"> cs_dst = get_domain_cap_set_from_domain_id s did </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 345 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 346 </font></span><font color="#ff00cc"> (s⦇</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 347 </font></span><font color="#ff00cc"> caps := caps0(did := (insert dst_cap cs_dst))</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 348 </font></span><font color="#ff00cc"> ⦈, True)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 349 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 350 </font></span><font color="#ff00cc"> (s, False)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 351 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 352 </font></span><font color="#006699"><strong>definition</strong></font> remove_cap_right <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ cap ⇒ right ⇒ (State × bool)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 353 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"remove_cap_right s did rm_cap right_to_rm ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 354 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 355 </font></span><font color="#ff00cc"> caps0 = caps s;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 356 </font></span><font color="#ff00cc"> cs_dst = get_domain_cap_set_from_domain_id s did;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 357 </font></span><font color="#ff00cc"> cs_rest = {c. c∈cs_dst ∧ c≠rm_cap}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 358 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 359 </font></span><font color="#ff00cc"> if(rm_cap ∈ get_domain_cap_set_from_domain_id s did </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 360 </font></span><font color="#ff00cc"> ∧ REMOVE ∈ rights rm_cap</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 361 </font></span><font color="#ff00cc"> ∧ right_to_rm ∈ rights rm_cap</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 362 </font></span><font color="#ff00cc"> ∧ REMOVE = right_to_rm</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 363 </font></span><font color="#ff00cc"> ∧ {REMOVE} = rights rm_cap)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 364 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 365 </font></span><font color="#ff00cc"> (s⦇</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 366 </font></span><font color="#ff00cc"> caps := caps0(did := (cs_rest))</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 367 </font></span><font color="#ff00cc"> ⦈, True)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 368 </font></span><font color="#ff00cc"> else if(</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 369 </font></span><font color="#ff00cc"> rm_cap ∈ get_domain_cap_set_from_domain_id s did </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 370 </font></span><font color="#ff00cc"> ∧ REMOVE ∈ rights rm_cap</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 371 </font></span><font color="#ff00cc"> ∧ right_to_rm ∈ rights rm_cap</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 372 </font></span><font color="#ff00cc"> )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 373 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 374 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 375 </font></span><font color="#ff00cc"> new_cap = ⦇ target = target rm_cap,</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 376 </font></span><font color="#ff00cc"> rights = (rights rm_cap) - {right_to_rm}⦈</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 377 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 378 </font></span><font color="#ff00cc"> (s⦇</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 379 </font></span><font color="#ff00cc"> caps := caps0(did := (insert new_cap cs_rest))</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 380 </font></span><font color="#ff00cc"> ⦈, True)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 381 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 382 </font></span><font color="#ff00cc"> (s, False)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 383 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 384 </font></span><font color="#006699"><strong>definition</strong></font> system_init <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config ⇒ State"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 385 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"system_init sc ≡ ⦇</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 386 </font></span><font color="#ff00cc"> caps = (λ x. {}),</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 387 </font></span><font color="#ff00cc"> e_msgs = (λ x. {}),</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 388 </font></span><font color="#ff00cc"> e_buf_size = (λ x. None),</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 389 </font></span><font color="#ff00cc"> domain_endpoint = e_listener(commconf sc)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 390 </font></span><font color="#ff00cc"> ⦈"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 391 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 392 </font></span><font color="#006699"><strong>subsection</strong></font><font color="#6600cc">{* Instantiation and Its Proofs of Security Model *}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 393 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 394 </font></span><font color="#006699"><strong>consts</strong></font> sysconf <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Sys_Config"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 395 </font></span><font color="#006699"><strong>definition</strong></font> sys_config_witness <font color="#000000"><strong>::</strong></font> Sys_Config
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 396 </font></span> <font color="#009966"><strong>where</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 397 </font></span> <font color="#ff00cc">"sys_config_witness ≡ ⦇</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 398 </font></span><font color="#ff00cc"> domconf = ⦇ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 399 </font></span><font color="#ff00cc"> d_name = (λ x. None),</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 400 </font></span><font color="#ff00cc"> d_ep_set = (λ x. {})</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 401 </font></span><font color="#ff00cc"> ⦈ , </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 402 </font></span><font color="#ff00cc"> commconf = ⦇ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 403 </font></span><font color="#ff00cc"> e_max_buf_size = (λ x. None),</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 404 </font></span><font color="#ff00cc"> e_name = (λ x. None),</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 405 </font></span><font color="#ff00cc"> e_listener = (λ x. None)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 406 </font></span><font color="#ff00cc"> ⦈ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 407 </font></span><font color="#ff00cc"> ⦈"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 408 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 409 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 410 </font></span><font color="#006699"><strong>consts</strong></font> s0t <font color="#000000"><strong>::</strong></font> State
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 411 </font></span><font color="#006699"><strong>definition</strong></font> s0t_witness <font color="#000000"><strong>::</strong></font> State
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 412 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"s0t_witness ≡ system_init sysconf"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 413 </font></span><font color="#006699"><strong>specification</strong></font> <font color="#000000"><strong>(</strong></font>s0t<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 414 </font></span> s0t_init<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s0t = system_init sysconf"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 415 </font></span> <font color="#006699"><strong>by</strong></font> simp
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 416 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 417 </font></span><font color="#006699"><strong>definition</strong></font> exec_event <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ Event ⇒ State"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 418 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"exec_event s e ≡</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 419 </font></span><font color="#ff00cc"> case e of Client_Lookup_Endpoint_Name did ename ⇒ fst (client_lookup_endpoint_name sysconf s did ename)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 420 </font></span><font color="#ff00cc"> | Send_Queuing_Message did eid m ⇒ fst (send_queuing_message s did eid m)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 421 </font></span><font color="#ff00cc"> | Receive_Queuing_Message did eid ⇒ fst (receive_queuing_message s did eid)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 422 </font></span><font color="#ff00cc"> | Get_My_Endpoints_Set did ⇒ fst (get_my_endpoints_set s did)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 423 </font></span><font color="#ff00cc"> | Get_Caps did ⇒fst (get_caps s did)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 424 </font></span><font color="#ff00cc"> | Grant_Endpoint_Cap did grant_cap dst_cap ⇒ fst (grant_endpoint_cap s did grant_cap dst_cap)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 425 </font></span><font color="#ff00cc"> | Remove_Cap_Right did dst_cap right_to_rm ⇒ fst (remove_cap_right s did dst_cap right_to_rm)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 426 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 427 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 428 </font></span><font color="#006699"><strong>definition</strong></font> domain_of_event <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"Event ⇒ domain_id option"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 429 </font></span> <font color="#009966"><strong>where</strong></font> <font color="#ff00cc">"domain_of_event e ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 430 </font></span><font color="#ff00cc"> case e of Client_Lookup_Endpoint_Name did ename ⇒ Some did</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 431 </font></span><font color="#ff00cc"> | Send_Queuing_Message did eid m ⇒ Some did</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 432 </font></span><font color="#ff00cc"> | Receive_Queuing_Message did eid ⇒ Some did</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 433 </font></span><font color="#ff00cc"> | Get_My_Endpoints_Set did ⇒ Some did</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 434 </font></span><font color="#ff00cc"> | Get_Caps did ⇒ Some did</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 435 </font></span><font color="#ff00cc"> | Grant_Endpoint_Cap did grant_cap dst_cap ⇒ Some did</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 436 </font></span><font color="#ff00cc"> | Remove_Cap_Right did dst_cap right_to_rm ⇒ Some did</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 437 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 438 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 439 </font></span><font color="#006699"><strong>definition</strong></font> vpeq1 <font color="#000000"><strong>::</strong></font> <font color="#ff00cc">"State ⇒ domain_id ⇒ State ⇒ bool"</font> <font color="#000000"><strong>(</strong></font><font color="#ff00cc">"(_ ∼ _ ∼ _)"</font><font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 440 </font></span> <font color="#009966"><strong>where</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 441 </font></span> <font color="#ff00cc">"vpeq1 s d t ≡ </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 442 </font></span><font color="#ff00cc"> let</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 443 </font></span><font color="#ff00cc"> cs1 = get_domain_cap_set_from_domain_id s d;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 444 </font></span><font color="#ff00cc"> cs2 = get_domain_cap_set_from_domain_id t d;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 445 </font></span><font color="#ff00cc"> dom_eps1 = get_endpoints_of_domain s d;</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 446 </font></span><font color="#ff00cc"> dom_eps2 = get_endpoints_of_domain t d</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 447 </font></span><font color="#ff00cc"> in</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 448 </font></span><font color="#ff00cc"> if(cs1 = cs2</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 449 </font></span><font color="#ff00cc"> ∧ (∀v. interferes v s d ⟷ interferes v t d)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 450 </font></span><font color="#ff00cc"> ∧ dom_eps1 = dom_eps2</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 451 </font></span><font color="#ff00cc"> ∧ (∀ep. ep∈dom_eps1 </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 452 </font></span><font color="#ff00cc"> ⟶ get_msg_set_from_endpoint_id s ep = get_msg_set_from_endpoint_id t ep )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 453 </font></span><font color="#ff00cc"> )</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 454 </font></span><font color="#ff00cc"> then</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 455 </font></span><font color="#ff00cc"> True</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 456 </font></span><font color="#ff00cc"> else</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 457 </font></span><font color="#ff00cc"> False</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 458 </font></span><font color="#ff00cc"> "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 459 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 460 </font></span><font color="#006699"><strong>declare</strong></font> vpeq1_def <font color="#000000"><strong>[</strong></font>cong<font color="#000000"><strong>]</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 461 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 462 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 463 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 464 </font></span><font color="#006699"><strong>lemma</strong></font> vpeq1_transitive_lemma <font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀ s t r d. (vpeq1 s d t) ∧ (vpeq1 t d r) ⟶ (vpeq1 s d r)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 465 </font></span> <font color="#006699"><strong>using</strong></font> vpeq1_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 466 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 467 </font></span><font color="#006699"><strong>lemma</strong></font> vpeq1_symmetric_lemma <font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀ s t d. (vpeq1 s d t) ⟶ (vpeq1 t d s)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 468 </font></span> <font color="#006699"><strong>using</strong></font> vpeq1_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 469 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 470 </font></span><font color="#006699"><strong>lemma</strong></font> vpeq1_reflexive_lemma <font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀ s d. (vpeq1 s d s)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 471 </font></span> <font color="#006699"><strong>using</strong></font> vpeq1_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 472 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 473 </font></span><font color="#006699"><strong>lemma</strong></font> interf_reflexive_lemma <font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀d s. interferes d s d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 474 </font></span> <font color="#006699"><strong>using</strong></font> interferes_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 475 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 476 </font></span><font color="#006699"><strong>lemma</strong></font> policy_respect_lemma <font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀v u s t. (s ∼ u ∼ t)</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 477 </font></span><font color="#ff00cc"> ⟶ (interferes v s u = interferes v t u)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 478 </font></span> <font color="#006699"><strong>using</strong></font> vpeq1_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 479 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 480 </font></span><font color="#006699"><strong>lemma</strong></font> reachable_top<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀ s a. (SM.reachable0 s0t exec_event) s ⟶ (∃s'. s' = exec_event s a)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 481 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 482 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 483 </font></span> <font color="#0099ff"><strong>fix</strong></font> s a
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 484 </font></span> <font color="#0099ff"><strong>assume</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(SM.reachable0 s0t exec_event) s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 485 </font></span> <font color="#006699"><strong>have</strong></font> <font color="#ff00cc">"(∃s'. s' = exec_event s a)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 486 </font></span> <font color="#006699"><strong>proof</strong></font> <font color="#000000"><strong>(</strong></font>induct a<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 487 </font></span> <font color="#0099ff"><strong>case</strong></font> <font color="#000000"><strong>(</strong></font>Client_Lookup_Endpoint_Name x<font color="#000000"><strong>)</strong></font> <font color="#0099ff"><strong>show</strong></font> ?case
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 488 </font></span> <font color="#006699"><strong>apply</strong></font> <font color="#000000"><strong>(</strong></font>induct x<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 489 </font></span> <font color="#006699"><strong>by</strong></font> <font color="#000000"><strong>(</strong></font>simp add<font color="#000000"><strong>:</strong></font> exec_event_def<font color="#000000"><strong>)</strong></font> <font color="#000000"><strong>+</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 490 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 491 </font></span> <font color="#0099ff"><strong>case</strong></font> <font color="#000000"><strong>(</strong></font>Send_Queuing_Message x1a x2 x3a<font color="#000000"><strong>)</strong></font> <font color="#0099ff"><strong>show</strong></font> ?case
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 492 </font></span> <font color="#006699"><strong>apply</strong></font> <font color="#000000"><strong>(</strong></font>induct x1a<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 493 </font></span> <font color="#006699"><strong>by</strong></font> <font color="#000000"><strong>(</strong></font>simp add<font color="#000000"><strong>:</strong></font> exec_event_def<font color="#000000"><strong>)</strong></font> <font color="#000000"><strong>+</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 494 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 495 </font></span> <font color="#0099ff"><strong>case</strong></font> <font color="#000000"><strong>(</strong></font>Receive_Queuing_Message x<font color="#000000"><strong>)</strong></font> <font color="#0099ff"><strong>show</strong></font> ?case
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 496 </font></span> <font color="#006699"><strong>apply</strong></font> <font color="#000000"><strong>(</strong></font>induct x<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 497 </font></span> <font color="#006699"><strong>by</strong></font> <font color="#000000"><strong>(</strong></font>simp add<font color="#000000"><strong>:</strong></font> exec_event_def<font color="#000000"><strong>)</strong></font> <font color="#000000"><strong>+</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 498 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 499 </font></span> <font color="#0099ff"><strong>case</strong></font> <font color="#000000"><strong>(</strong></font>Get_My_Endpoints_Set x<font color="#000000"><strong>)</strong></font> <font color="#0099ff"><strong>show</strong></font> ?case
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 500 </font></span> <font color="#006699"><strong>apply</strong></font> <font color="#000000"><strong>(</strong></font>induct x<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 501 </font></span> <font color="#006699"><strong>by</strong></font> <font color="#000000"><strong>(</strong></font>simp add<font color="#000000"><strong>:</strong></font> exec_event_def<font color="#000000"><strong>)</strong></font> <font color="#000000"><strong>+</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 502 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 503 </font></span> <font color="#0099ff"><strong>case</strong></font> <font color="#000000"><strong>(</strong></font>Get_Caps x <font color="#000000"><strong>)</strong></font> <font color="#0099ff"><strong>show</strong></font> ?case
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 504 </font></span> <font color="#006699"><strong>apply</strong></font> <font color="#000000"><strong>(</strong></font>induct x<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 505 </font></span> <font color="#006699"><strong>by</strong></font> <font color="#000000"><strong>(</strong></font>simp add<font color="#000000"><strong>:</strong></font> exec_event_def<font color="#000000"><strong>)</strong></font> <font color="#000000"><strong>+</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 506 </font></span> <font color="#0099ff"><strong>case</strong></font> <font color="#000000"><strong>(</strong></font>Grant_Endpoint_Cap x1a x2 x3a <font color="#000000"><strong>)</strong></font> <font color="#0099ff"><strong>show</strong></font> ?case
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 507 </font></span> <font color="#006699"><strong>apply</strong></font> <font color="#000000"><strong>(</strong></font>induct x1a<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 508 </font></span> <font color="#006699"><strong>by</strong></font> <font color="#000000"><strong>(</strong></font>simp add<font color="#000000"><strong>:</strong></font> exec_event_def<font color="#000000"><strong>)</strong></font> <font color="#000000"><strong>+</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 509 </font></span> <font color="#0099ff"><strong>case</strong></font> <font color="#000000"><strong>(</strong></font>Remove_Cap_Right x1a x2 <font color="#000000"><strong>)</strong></font> <font color="#0099ff"><strong>show</strong></font> ?case
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 510 </font></span> <font color="#006699"><strong>apply</strong></font> <font color="#000000"><strong>(</strong></font>induct x1a<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 511 </font></span> <font color="#006699"><strong>by</strong></font> <font color="#000000"><strong>(</strong></font>simp add<font color="#000000"><strong>:</strong></font> exec_event_def<font color="#000000"><strong>)</strong></font> <font color="#000000"><strong>+</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 512 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 513 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 514 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 515 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 516 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 517 </font></span><font color="#006699"><strong>declare</strong></font> Let_def <font color="#000000"><strong>[</strong></font>cong<font color="#000000"><strong>]</strong></font> <font color="#009966"><strong>and</strong></font> vpeq1_def<font color="#000000"><strong>[</strong></font>cong<font color="#000000"><strong>]</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 518 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 519 </font></span><font color="#006699"><strong>interpretation</strong></font> SM_enabled
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 520 </font></span> s0t exec_event domain_of_event vpeq1 interferes
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 521 </font></span> <font color="#006699"><strong>using</strong></font> vpeq1_transitive_lemma vpeq1_symmetric_lemma vpeq1_reflexive_lemma
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 522 </font></span> interf_reflexive_lemma policy_respect_lemma reachable_top
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 523 </font></span> SM.intro<font color="#000000"><strong>[</strong></font>of vpeq1 interferes<font color="#000000"><strong>]</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 524 </font></span> SM_enabled_axioms.intro<font color="#000000"><strong>[</strong></font>of s0t exec_event<font color="#000000"><strong>]</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 525 </font></span> SM_enabled.intro<font color="#000000"><strong>[</strong></font>of vpeq1 interferes s0t exec_event<font color="#000000"><strong>]</strong></font> <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 526 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 527 </font></span><font color="#006699"><strong>subsection</strong></font><font color="#6600cc">{* Some lemmas of security proofs *}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 528 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 529 </font></span><font color="#006699"><strong>subsection</strong></font><font color="#6600cc">{* Concrete unwinding condition of "local respect" *}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 530 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 531 </font></span><font color="#006699"><strong>subsubsection</strong></font><font color="#6600cc">{*proving "client lookup endpoint name" satisfying the "local respect" property*}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 532 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 533 </font></span> <font color="#006699"><strong>lemma</strong></font> client_lookup_endpoint_name_lcl_resp<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 534 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 535 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 536 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (client_lookup_endpoint_name sysconf s did ename)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 537 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 538 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 539 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 540 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s = s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 541 </font></span> <font color="#006699"><strong>by</strong></font> <font color="#000000"><strong>(</strong></font>simp add<font color="#000000"><strong>:</strong></font> p2 client_lookup_endpoint_name_def p1<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 542 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 543 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 544 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 545 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 546 </font></span> <font color="#006699"><strong>lemma</strong></font> client_lookup_endpoint_name_lcl_resp_e<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 547 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 548 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"a = (Client_Lookup_Endpoint_Name did ename)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 549 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes (the (domain_of_event a)) s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 550 </font></span> <font color="#009966"><strong>and</strong></font> p3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = exec_event s a"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 551 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 552 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 553 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 554 </font></span> <font color="#006699"><strong>have</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(the (domain_of_event a)) = did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 555 </font></span> <font color="#006699"><strong>using</strong></font> p1 domain_of_event_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 556 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (client_lookup_endpoint_name sysconf s did ename)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 557 </font></span> <font color="#006699"><strong>using</strong></font> p1 p3 exec_event_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 558 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 559 </font></span> <font color="#006699"><strong>using</strong></font> p2 a0 <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 560 </font></span> <font color="#006699"><strong>have</strong></font> a3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 561 </font></span> <font color="#006699"><strong>using</strong></font> a1 a2 p0 client_lookup_endpoint_name_lcl_resp <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 562 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 563 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 564 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 565 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 566 </font></span> <font color="#006699"><strong>lemma</strong></font> client_lookup_endpoint_name_lcrsp_e<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"dynamic_local_respect_e (Client_Lookup_Endpoint_Name did ename)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 567 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 568 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 569 </font></span> <font color="#006699"><strong>have</strong></font> <font color="#ff00cc">"∀d s. reachable0 s </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 570 </font></span><font color="#ff00cc"> ∧ ¬(interferes (the (domain_of_event (Client_Lookup_Endpoint_Name did ename))) s d) </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 571 </font></span><font color="#ff00cc"> ⟶ (s ∼ d ∼ (exec_event s (Client_Lookup_Endpoint_Name did ename)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 572 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 573 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 574 </font></span> <font color="#0099ff"><strong>fix</strong></font> d s
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 575 </font></span> <font color="#0099ff"><strong>assume</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 576 </font></span> <font color="#0099ff"><strong>assume</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">" ¬(interferes (the (domain_of_event (Client_Lookup_Endpoint_Name did ename))) s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 577 </font></span> <font color="#006699"><strong>have</strong></font> <font color="#ff00cc">"(s ∼ d ∼ (exec_event s (Client_Lookup_Endpoint_Name did ename)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 578 </font></span> <font color="#006699"><strong>using</strong></font> p1 p2 client_lookup_endpoint_name_lcl_resp_e <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 579 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 580 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 581 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 582 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 583 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 584 </font></span> <font color="#006699"><strong>using</strong></font> dynamic_local_respect_e_def <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 585 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 586 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 587 </font></span><font color="#006699"><strong>subsubsection</strong></font><font color="#6600cc">{*proving "send queuing message" satisfying the "local respect" property*}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 588 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 589 </font></span> <font color="#006699"><strong>lemma</strong></font> send_queuing_message_notchg_domain_cap_set<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 590 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 591 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 592 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (send_queuing_message s did eid m)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 593 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 594 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 595 </font></span> <font color="#006699"><strong>proof</strong></font> <font color="#000000"><strong>(</strong></font>cases <font color="#ff00cc">"(get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 596 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font><font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 597 </font></span> <font color="#0099ff"><strong>assume</strong></font> b0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 598 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 599 </font></span> <font color="#006699"><strong>have</strong></font> b1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 600 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 601 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 602 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 603 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 604 </font></span> <font color="#0099ff"><strong>assume</strong></font> b0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬ (get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 605 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 606 </font></span> <font color="#006699"><strong>have</strong></font> b1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s = s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 607 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 608 </font></span> <font color="#006699"><strong>have</strong></font> b2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 609 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 610 </font></span> <font color="#006699"><strong>using</strong></font> b1 get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 611 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 612 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 613 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 614 </font></span> <font color="#006699"><strong>lemma</strong></font> send_queuing_message_notchg_policy<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 615 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 616 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (send_queuing_message s did eid m)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 617 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"(∀v. interferes v s d ⟷ interferes v s' d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 618 </font></span> <font color="#006699"><strong>proof</strong></font> <font color="#000000"><strong>(</strong></font>cases <font color="#ff00cc">"(get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 619 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font><font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 620 </font></span> <font color="#0099ff"><strong>assume</strong></font> b0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 621 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 622 </font></span> <font color="#006699"><strong>have</strong></font> b1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 623 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 624 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 625 </font></span> <font color="#006699"><strong>have</strong></font> b2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀v. get_domain_cap_set_from_domain_id s v </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 626 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' v"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 627 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 628 </font></span> <font color="#006699"><strong>have</strong></font> b3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(∀v. interferes v s d ⟷ interferes v s' d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 629 </font></span> <font color="#006699"><strong>using</strong></font> b1 b2 interferes_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 630 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 631 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 632 </font></span> <font color="#0099ff"><strong>assume</strong></font> b0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬ (get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 633 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 634 </font></span> <font color="#006699"><strong>have</strong></font> b1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s = s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 635 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 636 </font></span> <font color="#006699"><strong>have</strong></font> b2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(∀v. interferes v s d ⟷ interferes v s' d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 637 </font></span> <font color="#006699"><strong>using</strong></font> b1 interferes_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 638 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 639 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 640 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 641 </font></span> <font color="#006699"><strong>lemma</strong></font> send_queuing_message_notchg_dom_eps<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 642 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 643 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (send_queuing_message s did eid m)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 644 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s d = get_endpoints_of_domain s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 645 </font></span> <font color="#006699"><strong>proof</strong></font> <font color="#000000"><strong>(</strong></font>cases <font color="#ff00cc">"(get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 646 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font><font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 647 </font></span> <font color="#0099ff"><strong>assume</strong></font> b0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 648 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 649 </font></span> <font color="#006699"><strong>have</strong></font> b1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 650 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 651 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 652 </font></span> <font color="#006699"><strong>have</strong></font> b2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"domain_endpoint s = domain_endpoint s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 653 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 654 </font></span> <font color="#006699"><strong>have</strong></font> b3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 655 </font></span><font color="#ff00cc"> = get_endpoints_of_domain s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 656 </font></span> <font color="#006699"><strong>using</strong></font> b2 get_endpoints_of_domain_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 657 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 658 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 659 </font></span> <font color="#0099ff"><strong>assume</strong></font> b0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬ (get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 660 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 661 </font></span> <font color="#006699"><strong>have</strong></font> b1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s = s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 662 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 663 </font></span> <font color="#006699"><strong>have</strong></font> b2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 664 </font></span><font color="#ff00cc"> = get_endpoints_of_domain s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 665 </font></span> <font color="#006699"><strong>using</strong></font> b1 get_endpoints_of_domain_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 666 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 667 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 668 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 669 </font></span> <font color="#006699"><strong>lemma</strong></font> send_queuing_message_notchg_ep_msgs<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 670 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 671 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 672 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (send_queuing_message s did eid m)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 673 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"(∀ep. ep∈get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 674 </font></span><font color="#ff00cc"> ⟶ get_msg_set_from_endpoint_id s ep = get_msg_set_from_endpoint_id s' ep )"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 675 </font></span> <font color="#006699"><strong>proof</strong></font> <font color="#000000"><strong>(</strong></font>cases <font color="#ff00cc">"(get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 676 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font><font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 677 </font></span> <font color="#0099ff"><strong>assume</strong></font> b0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 678 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 679 </font></span> <font color="#006699"><strong>have</strong></font> b1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 680 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 681 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 682 </font></span> <font color="#006699"><strong>have</strong></font> b2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"domain_endpoint s = domain_endpoint s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 683 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 684 </font></span> <font color="#006699"><strong>have</strong></font> b3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀e. e≠eid</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 685 </font></span><font color="#ff00cc"> ⟶ ((e_msgs s) e) = ((e_msgs s') e)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 686 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 687 </font></span> <font color="#006699"><strong>have</strong></font> b4<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"domain_endpoint s = domain_endpoint s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 688 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 689 </font></span> <font color="#006699"><strong>have</strong></font> b5<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 690 </font></span><font color="#ff00cc"> = get_endpoints_of_domain s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 691 </font></span> <font color="#006699"><strong>using</strong></font> b2 get_endpoints_of_domain_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 692 </font></span> <font color="#006699"><strong>have</strong></font> b6<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(the (get_domain_id_from_endpoint s eid)) ≠ d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 693 </font></span> <font color="#006699"><strong>using</strong></font> b0 p1 <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 694 </font></span> <font color="#006699"><strong>have</strong></font> b7<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(the ((domain_endpoint s) eid)) ≠ d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 695 </font></span> <font color="#006699"><strong>using</strong></font> b6 get_domain_id_from_endpoint_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 696 </font></span> <font color="#006699"><strong>have</strong></font> b8<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"eid ∉ get_endpoints_of_domain s d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 697 </font></span> <font color="#006699"><strong>using</strong></font> b7 b6 get_endpoints_of_domain_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 698 </font></span> <font color="#006699"><strong>have</strong></font> b9<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀ep. ep∈get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 699 </font></span><font color="#ff00cc"> ⟶ ((e_msgs s) ep) = ((e_msgs s') ep)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 700 </font></span> <font color="#006699"><strong>using</strong></font> b8 b3 <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 701 </font></span> <font color="#006699"><strong>have</strong></font> b10<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀ep. ep∈get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 702 </font></span><font color="#ff00cc"> ⟶ get_msg_set_from_endpoint_id s ep = get_msg_set_from_endpoint_id s' ep"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 703 </font></span> <font color="#006699"><strong>using</strong></font> b9 get_msg_set_from_endpoint_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 704 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 705 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 706 </font></span> <font color="#0099ff"><strong>assume</strong></font> b0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬ (get_domain_id_from_endpoint s eid ≠ None </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 707 </font></span><font color="#ff00cc"> ∧ interferes did s (the (get_domain_id_from_endpoint s eid)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 708 </font></span> <font color="#006699"><strong>have</strong></font> b1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s = s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 709 </font></span> <font color="#006699"><strong>using</strong></font> b0 p2 send_queuing_message_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 710 </font></span> <font color="#006699"><strong>have</strong></font> b2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(∀ep. ep∈get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 711 </font></span><font color="#ff00cc"> ⟶ get_msg_set_from_endpoint_id s ep = get_msg_set_from_endpoint_id s' ep )"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 712 </font></span> <font color="#006699"><strong>using</strong></font> b1 <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 713 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 714 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 715 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 716 </font></span> <font color="#006699"><strong>lemma</strong></font> send_queuing_message_lcl_resp<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 717 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 718 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 719 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (send_queuing_message s did eid m)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 720 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 721 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 722 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 723 </font></span> <font color="#006699"><strong>have</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"did ≠ d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 724 </font></span> <font color="#006699"><strong>using</strong></font> p1 interferes_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 725 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 726 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 727 </font></span> <font color="#006699"><strong>using</strong></font> p0 p1 p2 send_queuing_message_notchg_domain_cap_set <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 728 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(∀v. interferes v s d ⟷ interferes v s' d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 729 </font></span> <font color="#006699"><strong>using</strong></font> p0 p1 p2 send_queuing_message_notchg_policy <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 730 </font></span> <font color="#006699"><strong>have</strong></font> a3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s d = get_endpoints_of_domain s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 731 </font></span> <font color="#006699"><strong>using</strong></font> p0 p1 p2 send_queuing_message_notchg_dom_eps <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 732 </font></span> <font color="#006699"><strong>have</strong></font> a4<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(∀ep. ep∈get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 733 </font></span><font color="#ff00cc"> ⟶ get_msg_set_from_endpoint_id s ep = get_msg_set_from_endpoint_id s' ep )"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 734 </font></span> <font color="#006699"><strong>using</strong></font> p0 p1 p2 send_queuing_message_notchg_ep_msgs <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 735 </font></span> <font color="#006699"><strong>have</strong></font> a5<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 736 </font></span> <font color="#006699"><strong>using</strong></font> a1 a2 a3 a4 <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 737 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 738 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 739 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 740 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 741 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 742 </font></span> <font color="#006699"><strong>lemma</strong></font> send_queuing_message_lcl_resp_e<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 743 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 744 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"a = Send_Queuing_Message did eid m"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 745 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes (the (domain_of_event a)) s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 746 </font></span> <font color="#009966"><strong>and</strong></font> p3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = exec_event s a"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 747 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 748 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 749 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 750 </font></span> <font color="#006699"><strong>have</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(the (domain_of_event a)) = did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 751 </font></span> <font color="#006699"><strong>using</strong></font> p1 domain_of_event_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 752 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (send_queuing_message s did eid m)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 753 </font></span> <font color="#006699"><strong>using</strong></font> p1 p3 exec_event_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 754 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 755 </font></span> <font color="#006699"><strong>using</strong></font> p2 a0 <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 756 </font></span> <font color="#006699"><strong>have</strong></font> a3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 757 </font></span> <font color="#006699"><strong>using</strong></font> a1 a2 p0 send_queuing_message_lcl_resp <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 758 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 759 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 760 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 761 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 762 </font></span> <font color="#006699"><strong>lemma</strong></font> send_queuing_message_lcl_lcrsp_e<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"dynamic_local_respect_e (Send_Queuing_Message did eid m)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 763 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 764 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 765 </font></span> <font color="#006699"><strong>have</strong></font> <font color="#ff00cc">"∀d s. reachable0 s </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 766 </font></span><font color="#ff00cc"> ∧ ¬(interferes (the (domain_of_event (Send_Queuing_Message did eid m))) s d) </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 767 </font></span><font color="#ff00cc"> ⟶ (s ∼ d ∼ (exec_event s (Send_Queuing_Message did eid m)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 768 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 769 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 770 </font></span> <font color="#0099ff"><strong>fix</strong></font> d s
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 771 </font></span> <font color="#0099ff"><strong>assume</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 772 </font></span> <font color="#0099ff"><strong>assume</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">" ¬(interferes (the (domain_of_event (Send_Queuing_Message did eid m))) s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 773 </font></span> <font color="#006699"><strong>have</strong></font> <font color="#ff00cc">"(s ∼ d ∼ (exec_event s (Send_Queuing_Message did eid m)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 774 </font></span> <font color="#006699"><strong>using</strong></font> p1 p2 send_queuing_message_lcl_resp_e <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 775 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 776 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 777 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 778 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 779 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 780 </font></span> <font color="#006699"><strong>using</strong></font> dynamic_local_respect_e_def <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 781 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 782 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 783 </font></span><font color="#006699"><strong>subsubsection</strong></font><font color="#6600cc">{*proving "receive queuing message" satisfying the "local respect" property*}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 784 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 785 </font></span><font color="#006699"><strong>lemma</strong></font> receive_queuing_message_notchg_domain_cap_set<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 786 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 787 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 788 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (receive_queuing_message s did eid)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 789 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 790 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 791 </font></span> <font color="#006699"><strong>proof</strong></font> <font color="#000000"><strong>(</strong></font>cases <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) = did"</font><font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 792 </font></span> <font color="#0099ff"><strong>assume</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) = did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 793 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 794 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 795 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 796 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 797 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 798 </font></span> <font color="#0099ff"><strong>assume</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) ≠ did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 799 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 800 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 801 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 802 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 803 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 804 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 805 </font></span><font color="#006699"><strong>lemma</strong></font> receive_queuing_message_notchg_policy<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 806 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 807 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 808 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (receive_queuing_message s did eid)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 809 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"(∀v. interferes v s d ⟷ interferes v s' d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 810 </font></span> <font color="#006699"><strong>proof</strong></font> <font color="#000000"><strong>(</strong></font>cases <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) = did"</font><font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 811 </font></span> <font color="#0099ff"><strong>assume</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) = did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 812 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 813 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 814 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 815 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀v. get_domain_cap_set_from_domain_id s v </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 816 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' v"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 817 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 818 </font></span> <font color="#006699"><strong>have</strong></font> a3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(∀v. interferes v s d ⟷ interferes v s' d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 819 </font></span> <font color="#006699"><strong>using</strong></font> a1 a2 interferes_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 820 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 821 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 822 </font></span> <font color="#0099ff"><strong>assume</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) ≠ did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 823 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s = s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 824 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 825 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(∀v. interferes v s d ⟷ interferes v s' d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 826 </font></span> <font color="#006699"><strong>using</strong></font> a1 interferes_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 827 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 828 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 829 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 830 </font></span><font color="#006699"><strong>lemma</strong></font> receive_queuing_message_notchg_dom_eps<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 831 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 832 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (receive_queuing_message s did eid)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 833 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s d = get_endpoints_of_domain s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 834 </font></span> <font color="#006699"><strong>proof</strong></font> <font color="#000000"><strong>(</strong></font>cases <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) = did"</font><font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 835 </font></span> <font color="#0099ff"><strong>assume</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) = did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 836 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 837 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 838 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 839 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"domain_endpoint s = domain_endpoint s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 840 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 841 </font></span> <font color="#006699"><strong>have</strong></font> a3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 842 </font></span><font color="#ff00cc"> = get_endpoints_of_domain s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 843 </font></span> <font color="#006699"><strong>using</strong></font> a1 a2 get_endpoints_of_domain_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 844 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 845 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 846 </font></span> <font color="#0099ff"><strong>assume</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) ≠ did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 847 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s = s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 848 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 849 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 850 </font></span><font color="#ff00cc"> = get_endpoints_of_domain s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 851 </font></span> <font color="#006699"><strong>using</strong></font> a1 get_endpoints_of_domain_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 852 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 853 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 854 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 855 </font></span><font color="#006699"><strong>lemma</strong></font> receive_queuing_message_notchg_ep_msgs<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 856 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 857 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 858 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (receive_queuing_message s did eid)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 859 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"(∀ep. ep∈get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 860 </font></span><font color="#ff00cc"> ⟶ get_msg_set_from_endpoint_id s ep = get_msg_set_from_endpoint_id s' ep )"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 861 </font></span> <font color="#006699"><strong>proof</strong></font> <font color="#000000"><strong>(</strong></font>cases <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) = did"</font><font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 862 </font></span> <font color="#0099ff"><strong>assume</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) = did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 863 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 864 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 865 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 866 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"domain_endpoint s = domain_endpoint s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 867 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 868 </font></span> <font color="#006699"><strong>have</strong></font> a3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 869 </font></span><font color="#ff00cc"> = get_endpoints_of_domain s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 870 </font></span> <font color="#006699"><strong>using</strong></font> a1 a2 get_endpoints_of_domain_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 871 </font></span> <font color="#006699"><strong>have</strong></font> a4<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀e. e≠eid</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 872 </font></span><font color="#ff00cc"> ⟶ ((e_msgs s) e) = ((e_msgs s') e)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 873 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 874 </font></span> <font color="#006699"><strong>have</strong></font> a5<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"d ≠ did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 875 </font></span> <font color="#006699"><strong>using</strong></font> p1 interferes_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 876 </font></span> <font color="#006699"><strong>have</strong></font> a6<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) ≠ d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 877 </font></span> <font color="#006699"><strong>using</strong></font> a5 a0 <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 878 </font></span> <font color="#006699"><strong>have</strong></font> a7<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(the ((domain_endpoint s) eid)) ≠ d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 879 </font></span> <font color="#006699"><strong>using</strong></font> a6 get_domain_id_from_endpoint_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 880 </font></span> <font color="#006699"><strong>have</strong></font> a8<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"eid ∉ get_endpoints_of_domain s d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 881 </font></span> <font color="#006699"><strong>using</strong></font> a7 a6 get_endpoints_of_domain_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 882 </font></span> <font color="#006699"><strong>have</strong></font> a9<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀ep. ep∈get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 883 </font></span><font color="#ff00cc"> ⟶ ((e_msgs s) ep) = ((e_msgs s') ep)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 884 </font></span> <font color="#006699"><strong>using</strong></font> a8 a4 <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 885 </font></span> <font color="#006699"><strong>have</strong></font> a10<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"∀ep. ep∈get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 886 </font></span><font color="#ff00cc"> ⟶ get_msg_set_from_endpoint_id s ep = get_msg_set_from_endpoint_id s' ep"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 887 </font></span> <font color="#006699"><strong>using</strong></font> a9 get_msg_set_from_endpoint_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 888 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 889 </font></span> <font color="#006699"><strong>next</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 890 </font></span> <font color="#0099ff"><strong>assume</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"the(get_domain_id_from_endpoint s eid) ≠ did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 891 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s = s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 892 </font></span> <font color="#006699"><strong>using</strong></font> a0 p2 receive_queuing_message_def get_domain_cap_set_from_domain_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 893 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(∀ep. ep∈get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 894 </font></span><font color="#ff00cc"> ⟶ get_msg_set_from_endpoint_id s ep = get_msg_set_from_endpoint_id s' ep )"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 895 </font></span> <font color="#006699"><strong>using</strong></font> a1 get_msg_set_from_endpoint_id_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 896 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 897 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 898 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 899 </font></span> <font color="#006699"><strong>lemma</strong></font> receive_queuing_message_lcl_resp<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 900 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 901 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 902 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (receive_queuing_message s did eid)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 903 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 904 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 905 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 906 </font></span> <font color="#006699"><strong>have</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"did ≠ d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 907 </font></span> <font color="#006699"><strong>using</strong></font> p1 interferes_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 908 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_domain_cap_set_from_domain_id s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 909 </font></span><font color="#ff00cc"> = get_domain_cap_set_from_domain_id s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 910 </font></span> <font color="#006699"><strong>using</strong></font> p0 p1 p2 receive_queuing_message_notchg_domain_cap_set <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 911 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(∀v. interferes v s d ⟷ interferes v s' d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 912 </font></span> <font color="#006699"><strong>using</strong></font> p0 p1 p2 receive_queuing_message_notchg_policy <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 913 </font></span> <font color="#006699"><strong>have</strong></font> a3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"get_endpoints_of_domain s d = get_endpoints_of_domain s' d"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 914 </font></span> <font color="#006699"><strong>using</strong></font> p0 p1 p2 receive_queuing_message_notchg_dom_eps <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 915 </font></span> <font color="#006699"><strong>have</strong></font> a4<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(∀ep. ep∈get_endpoints_of_domain s d </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 916 </font></span><font color="#ff00cc"> ⟶ get_msg_set_from_endpoint_id s ep = get_msg_set_from_endpoint_id s' ep )"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 917 </font></span> <font color="#006699"><strong>using</strong></font> p0 p1 p2 receive_queuing_message_notchg_ep_msgs <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 918 </font></span> <font color="#006699"><strong>have</strong></font> a5<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 919 </font></span> <font color="#006699"><strong>using</strong></font> a1 a2 a3 a4 <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 920 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 921 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 922 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 923 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 924 </font></span> <font color="#006699"><strong>lemma</strong></font> receive_queuing_message_lcl_resp_e<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 925 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 926 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"a = (Receive_Queuing_Message did eid)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 927 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes (the (domain_of_event a)) s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 928 </font></span> <font color="#009966"><strong>and</strong></font> p3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = exec_event s a"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 929 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 930 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 931 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 932 </font></span> <font color="#006699"><strong>have</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(the (domain_of_event a)) = did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 933 </font></span> <font color="#006699"><strong>using</strong></font> p1 domain_of_event_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 934 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (receive_queuing_message s did eid)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 935 </font></span> <font color="#006699"><strong>using</strong></font> p1 p3 exec_event_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 936 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 937 </font></span> <font color="#006699"><strong>using</strong></font> p2 a0 <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 938 </font></span> <font color="#006699"><strong>have</strong></font> a3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 939 </font></span> <font color="#006699"><strong>using</strong></font> a1 a2 p0 receive_queuing_message_lcl_resp <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 940 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 941 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 942 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 943 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 944 </font></span> <font color="#006699"><strong>lemma</strong></font> receive_queuing_message_lcrsp_e<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"dynamic_local_respect_e (Receive_Queuing_Message did eid)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 945 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 946 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 947 </font></span> <font color="#006699"><strong>have</strong></font> <font color="#ff00cc">"∀d s. reachable0 s </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 948 </font></span><font color="#ff00cc"> ∧ ¬(interferes (the (domain_of_event (Receive_Queuing_Message did eid))) s d) </font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 949 </font></span><font color="#ff00cc"> ⟶ (s ∼ d ∼ (exec_event s (Receive_Queuing_Message did eid)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 950 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 951 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 952 </font></span> <font color="#0099ff"><strong>fix</strong></font> d s
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 953 </font></span> <font color="#0099ff"><strong>assume</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s "</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 954 </font></span> <font color="#0099ff"><strong>assume</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">" ¬(interferes (the (domain_of_event (Receive_Queuing_Message did eid))) s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 955 </font></span> <font color="#006699"><strong>have</strong></font> <font color="#ff00cc">"(s ∼ d ∼ (exec_event s (Receive_Queuing_Message did eid)))"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 956 </font></span> <font color="#006699"><strong>using</strong></font> p1 p2 receive_queuing_message_lcl_resp_e <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 957 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 958 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 959 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 960 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 961 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 962 </font></span> <font color="#006699"><strong>using</strong></font> dynamic_local_respect_e_def <font color="#006699"><strong>by</strong></font> blast
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 963 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 964 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 965 </font></span><font color="#006699"><strong>subsubsection</strong></font><font color="#6600cc">{*proving "get my endpoints set" satisfying the "local respect" property*}</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 966 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 967 </font></span> <font color="#006699"><strong>lemma</strong></font> get_my_endpoints_set_lcl_resp<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 968 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 969 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 970 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (get_my_endpoints_set s did)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 971 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 972 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 973 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 974 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s = s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 975 </font></span> <font color="#006699"><strong>by</strong></font> <font color="#000000"><strong>(</strong></font>simp add<font color="#000000"><strong>:</strong></font> p2 get_my_endpoints_set_def p1<font color="#000000"><strong>)</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 976 </font></span> <font color="#006699"><strong>}</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 977 </font></span> <font color="#006699"><strong>then</strong></font> <font color="#0099ff"><strong>show</strong></font> ?thesis <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 978 </font></span> <font color="#006699"><strong>qed</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 979 </font></span>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 980 </font></span> <font color="#006699"><strong>lemma</strong></font> get_my_endpoints_set_lcl_resp_e<font color="#000000"><strong>:</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 981 </font></span> <font color="#009966"><strong>assumes</strong></font> p0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"reachable0 s"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 982 </font></span> <font color="#009966"><strong>and</strong></font> p1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"a = (Get_My_Endpoints_Set did)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 983 </font></span> <font color="#009966"><strong>and</strong></font> p2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes (the (domain_of_event a)) s d)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 984 </font></span> <font color="#009966"><strong>and</strong></font> p3<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = exec_event s a"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 985 </font></span> <font color="#009966"><strong>shows</strong></font> <font color="#ff00cc">"s ∼ d ∼ s'"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 986 </font></span> <font color="#006699"><strong>proof</strong></font> -
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 987 </font></span> <font color="#006699"><strong>{</strong></font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 988 </font></span> <font color="#006699"><strong>have</strong></font> a0<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"(the (domain_of_event a)) = did"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 989 </font></span> <font color="#006699"><strong>using</strong></font> p1 domain_of_event_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff990066"> 990 </font></span> <font color="#006699"><strong>have</strong></font> a1<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"s' = fst (get_my_endpoints_set s did)"</font>
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 991 </font></span> <font color="#006699"><strong>using</strong></font> p1 p3 exec_event_def <font color="#006699"><strong>by</strong></font> auto
<span style="background:#ffdbdbdb; border-right:solid 2px black; margin-right:5px; "><font color="#ff000000"> 992 </font></span> <font color="#006699"><strong>have</strong></font> a2<font color="#000000"><strong>:</strong></font> <font color="#ff00cc">"¬(interferes did s d)"</font>